naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurements

Inverse physics-informed neural networks (PINNs) are vulnerable to corrupted measurements because their usual squared data loss gives extreme residuals the largest gradients. naPINN learns a residual density without prescribing a distribution family and converts its scores into trainable per-measurement gates. The density is fitted on detached residuals; the gates reweight a conventional reconstruction loss, with a rejection cost preventing collapse. Across three exact-PDE benchmarks, naPINN roughly halves the error of tuned robust losses and outperforms six screening procedures. On real particle image velocimetry with a nominal Navier--Stokes model, it also outperforms direct learned-likelihood optimisation, although the two are competitive on exact synthetic benchmarks. Because the regimes differ beyond model fidelity, this reversal motivates, but does not establish, the value of separating density estimation and corruption decisions.